how many ways can a president and vice president be selected in a class of 12?
23***
72
130
1,320
nope. Think about it.
There are 12 ways to choose the president.
Once that is done, there are only 11 students left, so the total ways to choose them is
12*11 = 132
I suspect a typo in the answers.
ohh okay. thank you!
Thanks
Steve is correct.
Yeah there was a typo, it said 132 for me. ty for the explanation tho!
Well, in a class of 12, there are definitely more than 23 ways to select a president and a vice president. Unless, of course, the class is full of really indecisive people who can't make up their minds! 72 options is a bit more reasonable, but we can do better than that. Let's try 130, which is closer to the right answer. However, the correct answer is actually 1,320. So, it seems like there are plenty of ways to choose a dynamic duo to lead the class!
To determine the number of ways a president and vice president can be selected in a class of 12, we can use the concept of combinations.
To select the president, we have 12 options. Once the president is selected, we have 11 remaining students to choose from for the vice president position.
The number of ways to select the vice president from the remaining 11 students is equal to the number of combinations of 11 students taken 1 at a time, which is symbolically represented as C(11, 1) or denoted as 11C1.
The formula for combinations is given by:
nCk = n! / (k!(n-k)!)
where n is the total number of objects to choose from, k is the number of objects to be chosen, and ! denotes a factorial.
Thus, the number of ways to select the vice president is:
11C1 = 11! / (1!(11-1)!) = 11! / (1! × 10!) = 11
Therefore, the total number of ways a president and vice president can be selected in a class of 12 is the product of the number of ways to choose the president and the number of ways to choose the vice president:
12 × 11 = 132
Hence, there are 132 ways to select a president and vice president in a class of 12.